Repeat the pendulum experiment of the previous problem. Displace the mass 30° counter-clockwise (positive π/6 radians) from the vertical, only this time do not release the mass from rest. Instead, push the mass in the clockwise (negative) direction with enough negative angular velocity so that it spins around in a circle exactly one time before settling into a motion decaying to a stable equilibrium. The tricky part of this experiment is the fact that the stable equilibrium point is now θ = −2π, ω = 0.
a) Without using any technology, sketch graphs of θ versus t and ω versus t approximating the motion of the pendulum.
b) Without using any technology, sketch graphs of ω versus θ. Place ω on the vertical axis, θ on the horizontal axis. Note: This is a lot harder than it looks. We suggest that you work with a partner or a group and compare solutions before moving on to part c).
c) Select Gallery→pendulum in the PPLANE6 Setup window. Adjust the damping parameter to D = 0.1, and set the display window so that −10 ≤ θ ≤ 5 and −4 ≤ ω ≤ 4. Select Options→Solution direction→Forward and use the Keyboard input window to start a solution trajectory with initial condition θ(0) = π/6 rad and ω(0) = −2.5 rad/s. Compare this result with your hand-drawn solution in part b). Select Graph→Both and click your solution trajectory in the phase plane to produce plots of θ versus t and ω versus t. Compare these with your hand-drawn solutions in part a).
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.